Expansions
ICSE · Class 9 · Mathematics
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Expand (x + 3)²
What is the expansion of (2y - 5)²?
If (x + 4)² = x² + kx + 16, what is the value of k?
Calculate (11)² using the expansion formula
Sample Questions
Which of the following are correct expansions? (Select all correct answers)
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(a + 7)² = a² + 14a + 49, (3m - 2)² = 9m² - 12m + 4, (5 - n)² = 25 - 10n + n²
Correct: (a + 7)² = a² + 14a + 49 ✓, (3m - 2)² = 9m² - 12m + 4 ✓, (5 - n)² = 25 - 10n + n² ✓. Incorrect: (p + q)² should include 2pq term, (x - 1)² should be x² - 2x + 1
Find the value of (9)² using expansion
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81
Write 9 = 10 - 1, then (9)² = (10 - 1)² = 10² - 2(10)(1) + 1² = 100 - 20 + 1 = 81
What is the middle term coefficient in the expansion of (x + 5)²?
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10
(x + 5)² = x² + 10x + 25. The middle term is 10x, so the coefficient is 10. Using the formula 2ab where a = x, b = 5: 2(1)(5) = 10
Which expressions can be written as perfect squares? (Select all correct answers)
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x² + 8x + 16, y² - 6y + 9, m² - 10m + 25
Perfect squares: x² + 8x + 16 = (x + 4)², y² - 6y + 9 = (y - 3)², m² - 10m + 25 = (m - 5)². For perfect squares, check if b² = 4ac pattern holds
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